This volume contains the revised and completed notes of lectures given at theschool "Quantum Potential Theory: Structure and Applications to Physics," held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald from February 26 to March 10, 2007. Quantum potential theory studies noncommutative (or quantum) analogs of classical potential theory. These lectures provide an introduction tothis theory, concentrating on probabilistic potential theory and it quantum analogs, i.e. quantum Markov processes and semigroups, quantum random walks, Dirichlet forms on C* and von Neumann algebras, and boundary theory. Applications to quantum physics, in particular the filtering problem in quantum optics, are also presented. INDICE: Potential Theory in Classical Probability, Nicolas Privault.- Introduction to Random Walks on Noncommutative Spaces, Philippe Biane.- Interactions between Qantum Probability and Operator Space Theory, Quanhua Xu.- Dirichlet Forms on Noncommutative Spaces, Fabio Cipriani.- Applications of Controlled Quantum Processes in Quantum Optics, Luc Bouten.- Quantum Walks, Norio Konno.
- ISBN: 978-3-540-69364-2
- Editorial: Springer
- Encuadernacion: Rústica
- Páginas: 464
- Fecha Publicación: 01/10/2008
- Nº Volúmenes: 1
- Idioma: Inglés